A certain solution contains $2.1$ grams of salt per liter. How many liters of the solution would contain $25$ grams of salt? Round your answer, if necessary, to the nearest tenth.
Explanation: This is a density word problem. To solve it, we can use the following equation, which is the volume definition of density: ${\text{Density}}=\dfrac{{\text{Total quantity}}}{{\text{Volume}}}$ What do we know? The ${\text{density}}$ of salt in the solution is ${2.1}$ grams per liter. We want to have a total of ${25}$ grams of salt. This is the ${\text{total quantity}}$. What do we need to find? The ${\text{volume}}$ of solution that we need. Let's denote the volume as $ v$. Now we can plug ${\text{density}=2.1}$, ${\text{total quantity}=25}$, and ${\text{volume}=v}$ in the equation. $\begin{aligned} {\text{Density}}&=\dfrac{{\text{Total quantity}}}{{\text{Volume}}} \\\\ {2.1}&=\dfrac{{25}}{{v}} \\\\ {v}\cdot{2.1}&=\dfrac{{25}}{\cancel{{v}}}\cdot\cancel{{v}} \\\\ v&=\dfrac{{25}}{{2.1}}\approx{11.9} \end{aligned}$ We need approximately $11.9$ liters of the solution in order to have $25$ grams of salt.